Probability and Statistics
Probability Distributions
Discrete Distributions
- Bernoulli distribution
- Binomial distribution
- Poisson distribution
- Geometric distribution
- Uniform discrete distribution
Continuous Distributions
- Uniform distribution
- Normal (Gaussian) distribution
- Exponential distribution
- Beta distribution
- Gamma distribution
Distribution Properties
- Probability density function (PDF)
- Cumulative distribution function (CDF)
- Mean, variance, standard deviation
- Skewness and kurtosis
- Moments of distributions
Bayes' Theorem
Conditional Probability
- Definition of conditional probability
- Joint probability
- Marginal probability
- Chain rule
Bayes' Theorem
- Statement of Bayes' theorem
- Prior probability
- Likelihood
- Posterior probability
- Bayesian inference
Applications
- Naive Bayes classifier
- Bayesian networks
- Bayesian parameter estimation
- Medical diagnosis
Hypothesis Testing
Concepts
- Null hypothesis (H0)
- Alternative hypothesis (H1)
- Type I and Type II errors
- Significance level (α)
- p-value
- Power of a test
Common Tests
- t-test (one-sample, two-sample, paired)
- Chi-square test
- ANOVA
- Z-test
- Mann-Whitney U test
Test Selection
- Parametric vs non-parametric tests
- Assumptions for each test
- When to use which test
Confidence Intervals
Concepts
- Point estimates
- Interval estimates
- Confidence level
- Margin of error
Construction
- Confidence interval for mean (known variance)
- Confidence interval for mean (unknown variance)
- Confidence interval for proportion
- Bootstrap confidence intervals
Interpretation
- What confidence intervals mean
- Common misconceptions
- Relationship to hypothesis testing
Practice Questions
Test your understanding with the questions in the interactive quiz below (when available).
Resources
- "Introduction to Probability" by Blitzstein and Hwang
- "Think Bayes" by Allen Downey
- Scipy Statistics: https://docs.scipy.org/doc/scipy/reference/stats.html
- Khan Academy Statistics: https://www.khanacademy.org/math/statistics-probability